Based on the the large N duality relating Gromov-Witten theory on Calabi-Yau threefolds and Chern-Simons theory on three manifolds, Aganagic, Klemm, Marino, and Vafa proposed "the topological vertex", an algorithm computing open and closed Gromov-Witten invariants (in all genera) of any toric Calabi-Yau threefold. I will describe a mathematical theory of the topological vertex based on joint works with Jun Li, Kefeng Liu, and Jian Zhou.

Lecture #12372

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